No. You do not need a computer.
You would instead likely need a separate IC like the MAX232 (which Sparkfun should have) as a relay between you’re PIC and this device.
You’ll also need to provide power to the unit at +5V DC capable of 250mA.
The circuitry to support this is pretty trivial. The software to communicate properly is likely not. You will need to essentially provide an R232 driver to manage things like baud rate, and then develop software that controls the device - which armed with the command set and sparse datasheet provided here shouldn’t be impossible.

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